Wash six half-pint canning jars and place them on the rack in a boiling-water canner; cover with water by at least 1 inch and heat to a simmer. Prepare the lids according to the manufacturer’s directions.

Combine the 1 cup water and cranberries in a 4-quart saucepan and bring to a boil over medium-high heat; reduce the heat and simmer for 5–10 minutes, stirring occasionally, until most of the berries have burst.

Stir in the sugar until dissolved, return the mixture to a boil, and boil gently for 3 minutes, stirring frequently.

Remove the hot jars from the canner one at a time and fill with the hot sauce, leaving 1/4 inch of headspace. Remove air bubbles, wipe the rims clean, and apply the lids and bands fingertip-tight.

Return the jars to the canner, making sure they are covered by at least 1 inch of water, and process at a full boil for 15 minutes at 0–1,000 feet, 20 minutes at 1,001–3,000 feet, 25 minutes at 3,001–6,000 feet, or 30 minutes above 6,000 feet; start timing when the water returns to a full boil.

Turn off the heat, remove the canner lid, and let the jars rest in the canner for 5 minutes before lifting them onto a towel to cool undisturbed for 12–24 hours.

Check the seals, refrigerate any unsealed jars, and store sealed jars in a cool, dark place.